I train Cacoy doce pares/eskrido so we do a fair amount of work with curving strikes. My teacher's son is amazing at using them. Here's my thoughts on them:

When you strike someone continuously at medium range, one of the best things that can happen is for your opponent to start chasing your stick, cause if you're good at it they'll be getting hit many times before they actually catch you. How do you get someone to chase it? By overloading them and/or stunning them with an unexpected strike first. Some of the curving strikes I like best are abaniko hitting from what appears to be the opposite side of what would be expected. For example, I chamber my stick above the right shoulder, so they think forehand, but then I throw abaniko from the other side.

This^ paragraph assumes a low-level bad guy who's easily distracted, so feel free to not be super convinced. After all, we've all seen WEKAF sparring where 2 guys keep throwing whatever they want at each other, ignoring the ones that hit them. Anyway, moving on:

Curving strikes are weak, but when they hit the head they distract. When you hit the head with one, either forehand or backhand, you've set yourself up for a strong tigbas strike across the torso or leg. This is basically a variation of that knife drill where you go forehand stab high > turn palm over to forehand stomach cut > backhand stab high > turn palm over to backhand stomach cut. These work amazingly well against people with no experience.

Another use of the curving strike is adding a bit of offensive capability to a tail. A tail is a movement that bleeds extra kinetic energy after a strike into circular force, cause when you hit hard you follow through. Not all styles have this but hard stickfighting ones do, like DBMA stickfighting. Halfway through a tail, there's a moment where you can turn it into a curving strike. So let's say you miss with a hard shot from largo and your wrist is turning into a tail, and they lunge forward, so you turn it into a quick curving strike as you continue moving.

The bigger problem with the question of effectiveness of curving strikes, though, is that we're all talking about a lightweight doce pares stick which isn't really a great weapon for real life anyway. So, can curving strikes be used with real weapons? I'll mention a few where the answer is yes.

The saber: A saber with a good curve can use curving strikes to go around a parry and hit with the tip anyway. This can be done when a cut is en route and you see a parry come up, in a movement called a wrap or wind. It feels almost like casting the point into the target.

The double edge sword: Earlier I mentioned the knife drill where you go forehand stab high > turn palm over to forehand stomach cut > backhand stab high > turn palm over to backhand stomach cut. With a large double edge, this becomes high forehand with false edge > forehand low > high backhand with false edge > backhand low. Along the same lines, the false edge strike can also be a parry that leads into a power strike from the same side. For this reason, I like to snipe at the weapon hand using the false edge if I can, so I'm in a good followup position. The downside though is that you can be accidentally disarmed in this way if your grip is weak.

So far, the blade stuff I've mentioned applies to kurbata and songkiti, but not abaniko. This is cause abaniko with a blade would hit with the flat, so not very effective. But you can use that motion to slap an attack out of the way, and with a little practice, you'll find that just as their weapon is knocked offline, yours will be facing them point-first and close enough to stab by just extending the arm.

I'll kind of echo what fuzzy said. They've got a place as setup if you're using lightweight weapons. Of course I generally think lightweight impact weapons are ridiculous. They are just annoying, and won't drop an opponent.

You tend to see curving abanico style strikes in tournaments that count quantity of strikes to score. Some refs will actually have clickers and just tally point, regardless of decisiveness or power. Once again, I find this kind of silly.

Combatively, give me a longer stick with some weight to it. (At least that's what she says). I'll hit with power. If someone closes and I get his a couple of times with curving strikes or standard ones, I'll:

A. Laugh at them if they've got a lightweight stick, then wallop them with my tree trunk. CAVEMAN SMASH!

B. Check/punch the **** out of them to make some space for my power counter strikes.

C. Bail out, covering with power shots.

D. Get grapply.

Standing there and trading is just stupid tactically. It's also unrealistic combatively. I mean we've all seen fights, and what happens when someone is getting peppered? They rush to clinch, and try to make it a wrestling match. It surprises me that so many stickfighters seem to ignore this, even though we've all known about this tactic since second grade.

Curving strikes fit into this medio-corto range which is very difficult to maintain without it going to a grapple. So if you're only going to land a shot or two before its a clinch, why wouldn't you want to land full-power shots?